Indexes are created to improve performance when executing SQL commands such as SELECT. However, in some cases it is faster to perform a full scan even if there is an index, and in other cases it is not simply possible to determine which of the several indexes should be used to make it faster.

Disk access has the greatest impact on SQL execution speed. To estimate how much disk access is likely to be required for each of the several possible execution plans, the number of data items in each table, the amount of data spread in columns in the table, etc. are to be checked.

ANALYZE retrieves such information about the state of the table. It is desirable to run ANALYZE once on every table, and to run it again every time there is an update that significantly affects the number or distribution of data.

ANALYZE samples a small fraction of the data in a table and computes statistics, so it is quick to complete. When running ANALYZE on a table name, for example from the psql command line, the table owner or superuser can run ANALYZE.

If ANALYZE is specified as an option when running a VACUUM command, VACUUM and ANALYZE will run concurrently, but if no option is specified, only VACUUM will run.

Autovacuum performs an automatic VACUUM operation on tables that have reached a certain level of change, but it also runs ANALYZE at the same time.

So the correct answers are A, B, and E.